to say that something happened because of someone or something else (give credit or blame)

to say that an idea or quotation came from a specified source

Much of the marble coldness of Hester’s impression was to be attributed to the circumstance that her life had turned, in a great measure, from passion and feeling to thought.

For, as it was impossible to assign a reason for such distrust and abhorrence, so Mr. Dimmesdale, conscious that the poison of one morbid spot was infecting his heart’s entire substance, attributed all his presentiments to no other cause.

There are no more uses of "attribute" identified with this meaning, but check unspecified meaning below.

This last attribute, however, had been less carefully developed than his intellectual gifts, and was, in truth, rather a matter of shame than self-congratulation with him.

All merely graceful attributes are usually the most evanescent; nor does nature adorn the human ruin with blossoms of new beauty, that have their roots and proper nutriment only in the chinks and crevices of decay, as she sows wall-flowers over the ruined fortress of Ticonderoga.

In truth, he was startled, if not shocked, to find this attribute in the physician.

It kept him down on a level with the lowest; him, the man of ethereal attributes, whose voice the angels might else have listened to and answered!

Some attribute had departed from her, the permanence of which had been essential to keep her a woman.

Whoever touches it should look well to himself, or he may find the bargain to go hard against him, involving, if not his soul, yet many of its better attributes; its sturdy force, its courage and constancy, its truth, its self-reliance, and all that gives the emphasis to manly character.

But it was a remarkable attribute of this garb, and indeed, of the child’s whole appearance, that it irresistibly and inevitably reminded the beholder of the token which Hester Prynne was doomed to wear upon her bosom.

As he possessed no higher attribute, and neither sacrificed nor vitiated any spiritual endowment by devoting all his energies and ingenuities to subserve the delight and profit of his maw, it always pleased and satisfied me to hear him expatiate on fish, poultry, and butcher’s meat, and the most eligible methods of preparing them for the table.

With all these sterling attributes, thought Hester, the evil which she inherited from her mother must be great indeed, if a noble woman do not grow out of this elfish child.

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She remembered—betwixt a smile and a shudder—the talk of the neighbouring townspeople, who, seeking vainly elsewhere for the child’s paternity, and observing some of her odd attributes, had given out that poor little Pearl was a demon offspring: such as, ever since old Catholic times, had occasionally been seen on earth, through the agency of their mother’s sin, and to promote some foul and wicked purpose.